It is desirable in a variety of applications to determine various features of a target, such as the emissivity, area and temperature of the target, based upon multicolor radiant intensity measurements. For example, in ballistic missile defense and tactical air defense scenarios, the extraction of various features of a target from multicolor radiant intensity measurement facilitates the discrimination of an actual target from a decoy. Additionally, it would be useful to accurately determine the emissivity and temperature of various materials, such as composite materials, during wind tunnel testing. Still further, the determination of various features of a target based upon multicolor radiant intensity measurements can be employed in a wide variety of other applications including medical thermography, observational astronomy, astrophysics and the like.
Various techniques have therefore been developed in order to determine the emissivity, area and temperature of an object based upon multicolor radiant intensity measurements. For example, one technique measures the radiant intensity of an object at each of two different wavelengths, i.e., at two different colors. The temperature of the object is then derived based upon the ratio of the Planck radiances at each of the two wavelengths. Thereafter, the product of the emissivity and the area of the object, that is, the emissivity area, is derived by dividing the radiant intensity of the object that was measured by the Planck function evaluated at the temperature that was previously derived. However, the temperature that is derived is based entirely upon the emissivity of the object with the effects of reflected radiation being neglected. In instances in which the object under investigation is a black body, the temperature which is derived may be relatively unbiased. However, many objects are partially reflective such that the derivation of the temperature of the object based only on the emissivity of the object without taking into account the effects of reflected radiation may cause the temperature which is derived to be biased from the true temperature of the object. Since the emissivity area is dependent upon the temperature that has been derived, the bias that is reflected in the derivation of the temperature similarly causes the emissivity area that is derived to be biased from the true emissivity area of the object.
By way of example, a detector may be configured detect the radiant intensity of an object in two wavebands, namely, a first waveband centered at 6 microns and a second waveband centered at 11.5 microns; each waveband having a bandwidth of 1 micron. In one instance in which the actual temperature of the object was 300 Kelvin and the emissivity area of the object was actually 1×104 cm2, the temperature and the emissivity area of the object was then determined as described above for each of 64 different Monte Carlo trials. In this regard, the radiant intensity measurements include some amount of noise with the amount of noise being permitted to vary from trial to trial. As shown in FIGS. 1A and 1B, the temperature T and emissivity area EA, respectively, of the object that are derived vary somewhat from the actual temperature and emissivity area. In this example, the mean value of the temperature that was derived is 297.863 Kelvin in comparison to the actual temperature of the object being 300 Kelvin. Similarly, the mean of the emissivity area that is derived is 8.709×103 cm2 in comparison to an actual emissivity area of the object of 1×104 cm2. Moreover, the temperature and emissivity area values that were derived tend to vary from trial to trial with the standard deviation of the temperature values that are derived being 1.644 Kelvin and the standard deviation of the emissivity area values that are derived being 232.532 cm2 in this example.
FIG. 2 provides another graphical depiction of an example of this two-color technique in which the temperature T is plotted relative to the emissivity area EA. As shown by the square box 10, the actual temperature is 300 Kelvin and the actual emissivity area is 8,000 cm2. In contrast, the temperatures and emissivity areas that are derived are not only displaced from the actual temperature and emissivity area of the object, but are scattered across a range of temperatures and emissivity areas.
Another technique for extracting target features from multicolor radiant intensity measurements utilizes a three-color algorithm based upon radiant intensity measurements in three distinct wavebands. See, Spitzberg, R. M., Lincoln Laboratory, Tutorial on Target Phenomenology and Optical Discrimination for Midcourse Sensors, NMD Discrimination Working Group (Nov. 14, 2001). Based upon the radiant intensity measurements in each of the three wavebands, the emissivity, area and temperature of an object can be measured with less bias than those techniques that rely upon radiant intensity measurements within only two wavebands. However, the three-color algorithm generally requires separate regression or estimation of each of the emissivity, area and temperature. In this regard, conventional parameter estimation algorithms including the Levenburg Marquardt and Newton iterative solutions are generally required to separately estimate the emissivity, area and temperature of the object. While this three-color algorithm may serve to reduce the bias associated with the emissivity, area and temperature of the object, this three-color algorithm generally requires fairly substantial computational resources in order to separately estimate each of the three parameters, namely, emissivity, area and temperature.
Accordingly, it would be desirable to provide an improved technique for extracting target features, such as emissivity, area and temperature, from multicolor radiant intensity measurements. In particular, it would be desirable to provide an improved technique for determining the emissivity, area and temperature of an object from multicolor radiant intensity measurements which requires fewer computational resources and which introduces less bias into the determination.